keep the home fires burning

are your ears burning

Asked of somebody who was not present but was the topic of discussion.

book burning

Any mass destruction, removal, or recalling of books, motion pictures, broadcasts, or electronic works as a form of censorship, especially motivated by religious or political objections to the material.

bring home

To earn (money).

bring home the bacon

To have employment which provides remuneration to satisfy the basic needs of oneself and one's family.

broken home

A home in which the parents have separated or divorced.

burning question

An important and pertinent question that urgently requires an answer.

carbon burning

The nucleosynthesis process, in stars of greater than 8 solar mass that have exhausted their helium supply, in which carbon is converted to neon, sodium, magnesium and other elements.

charity begins at home

One should help the people closest to oneself before thinking of helping others.